Topics on Concentration Phenomena and Problems with Multiple Scales (Lecture Notes of the Unione Matematica Italiana)

The study of variational problems showing multi-scale behaviour with oscillation or concentration phenomena are a challenging topic of very active research. This volume includes lecture notes devoted to the asymptotic analysis of such problems when the multi-scale behaviour derives from scale separation in the passage from atomistic systems to continuous functionals, from competition between bulk and surface energies, from various types of homogenization processes (random, in perforated domains, on fractals), and to concentration effects in Ginzburg-Landau energies and in subcritical growth problems. Front Matter....Pages I-XI Front Matter....Pages 1-1 From discrete systems to continuous variational problems: an introduction....Pages 3-77 Relaxation for bulk and interfacial energies....Pages 79-138 Convergence of Dirichlet forms on fractals....Pages 139-188 Homogenization in perforated domains....Pages 189-208 Homogenization of random non stationary parabolic operators....Pages 209-230 Front Matter....Pages 232-232 Γ -convergence for concentration problems....Pages 233-266 Gamma-convergence of gradient flows and applications to Ginzburg-Landau vortex dynamics....Pages 267-292 PDE analysis of concentrating energies for the Ginzburg-Landau equation....Pages 293-314 Back Matter....Pages 315-317